Related papers: An unstructured finite element model for incompres…
This paper solves the discretised multiphase flow equations using tools and methods from machine-learning libraries. The idea comes from the observation that convolutional layers can be used to express a discretisation as a neural network…
New time integration methods are proposed for simulating incompressible multiphase flow in pipelines described by the one-dimensional two-fluid model. The methodology is based on 'half-explicit' Runge-Kutta methods, being explicit for the…
We introduce a novel positivity-preserving, parameter-free numerical stabilisation approach for high-order discontinuous spectral element approximations of compressible multi-species flows. The underlying stabilisation method is the…
Numerical simulations of two-phase flow and fluid structure interaction problems are of great interest in many environmental problems and engineering applications. To capture the complex physical processes involved in these problems, a high…
While various phase-field models have recently appeared for two-phase fluids with different densities, only some are known to be thermodynamically consistent, and practical stable schemes for their numerical simulation are lacking. In this…
In this paper, a novel fully-explicit weakly compressible solver is developed for solving incompressible two-phase flows. The two-phase flow is modelled by coupling the general pressure equation, momentum conservation equations and the…
Projection-based reduced order models rely on offline-online model decomposition, where the data-based energetic spatial basis is used in the expensive offline stage to obtain equations of reduced states that evolve in time during the…
We present a parametric finite element approximation of two-phase flow. This free boundary problem is given by the Navier--Stokes equations in the two phases, which are coupled via jump conditions across the interface. Using a novel…
In this article we consider the numerical modeling and simulation via the phase field approach of two-phase flows of different densities and viscosities in superposed fluid and porous layers. The model consists of the…
Reservoir simulators utilize numerical techniques to solve the governing equations of fluid flow in porous media and they are essential tool for oil and gas fields development. In practical reservoir simulation, the finite difference method…
Variable viscosity arises in many flow scenarios, often imposing numerical challenges. Yet, discretisation methods designed specifically for non-constant viscosity are few, and their analysis is even scarcer. In finite element methods for…
In this paper, we propose an improved phase field model for interface capturing in simulating two-phase incompressible flows. The model incorporates a second-order diffusion term, which utilizes a nonlinear coefficient to assess the degree…
We introduce a family of bi-grid schemes in finite elements for solving 2D incompressible Navier-Stokes equations in velocity and pressure $(u,p)$. The new schemes are based on projection methods and use two pairs of FEM spaces, a sparse…
In this paper, for the first time we propose two linear, decoupled, energy-stable numerical schemes for multi-component two-phase compressible flow with a realistic equation of state (e.g. Peng-Robinson equation of state). The methods are…
We consider the depth-integrated non-hydrostatic system derived by Yamazaki et al. An efficient formally second-order well-balanced hybrid finite volume finite difference numerical scheme is proposed. The scheme consists of a two-step…
This paper develops the high-order accurate entropy stable finite difference schemes for one- and two-dimensional special relativistic hydrodynamic equations. The schemes are built on the entropy conservative flux and the weighted…
For the incompressible Navier--Stokes system with variable density and viscosity, we propose and analyse an IMEX framework treating the convective and diffusive terms semi-implicitly. This extends to variable density and second order in…
Novel experimental modalities acquire spatially resolved velocity measurements for steady state and transient flows which are of interest for engineering and biological applications. One of the drawbacks of such high resolution velocity…
This paper proposes a fully implicit numerical scheme for immiscible incompressible two-phase flow in porous media taking into account gravity, capillary effects, and heterogeneity. The objective is to develop a fully implicit stable…
In this paper, we present a fast streamline-based numerical method for the two-phase flow equations in high-rate flooding scenarios for incompressible fluids in heterogeneous and anisotropic porous media. A fractional flow formulation is…